Observation 3: Low Density Ratios Help Off-Policy Methods. Looking at the left side of Fig. REF , a natural question might be why, as we increase \(\epsilon _{exp}\) , BC is consistent for a wider spectrum of \(\epsilon _{obs}\)  values. Observe that as we increase \(\epsilon _{exp}\) , the expert has a higher chance of making a mistake, bringing its trajectory distribution closer to that of the uniform policy and lowering the maximum density ratio between learner and expert trajectory distributions. As was established by [1]}, a low maximum density ratio is a sufficient condition for behavioral cloning to be consistent. This experiment appears to echo their theoretical results.
